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Magnetic Properties and Magnetocaloric Effect in
Gd100-xCox Thin Films
Mohamed Tadout, Charles-Henri Lambert, Mohammed Salah El Hadri,
Abdelilah Benyoussef, Mohammed Hamedoun, Mohammed Benaissa, Omar
Mounkachi, Stéphane Mangin
To cite this version:
Mohamed Tadout, Charles-Henri Lambert, Mohammed Salah El Hadri, Abdelilah Benyoussef,
Mo-hammed Hamedoun, et al.. Magnetic Properties and Magnetocaloric Effect in Gd100-xCox Thin
Films. Crystals, MDPI, 2019, 9 (6), pp.278. �10.3390/cryst9060278�. �hal-02185987�
crystals
ArticleMagnetic Properties and Magnetocaloric E
ffect in
Gd
100-x
Co
x
Thin Films
Mohamed Tadout1,2, Charles-Henri Lambert3,4, Mohammed Salah El Hadri3,5 ,
Abdelilah Benyoussef1,2, Mohammed Hamedoun2, Mohammed Benaissa1, Omar Mounkachi1,*
and Stéphane Mangin3
1 Laboratoire de Matière Condensée et Sciences Interdisciplinaires (LaMCScI), B.P. 1014, Faculty of
Science-Mohammed V University, 11000 Rabat, Morocco; tadout.mohamed@um5s.net.ma (M.T.); a.benyoussef@mascir.com (A.B.); benaissa@fsr.ac.ma (M.B.)
2 Materials and Nanomaterials Centre, Moroccan Foundation for Advanced Science, Innovation and
Reserarch, MAScIR, 11000 Rabat, Morocco; m.hamedoun@mascir.com
3 Institut Jean Lamour, UMR CNRS 7198, Université de Lorraine, 54000 Nancy, France;
charles-henri.lambert@mat.ethz.ch (C.-H.L.); melhadri@ucsd.edu (M.S.E.H.); stephane.mangin@univ-lorraine.fr (S.M.)
4 Laboratory for Magnetism and Interface Physics, Department of Materials, ETH Zurich,
8093 Zurich, Switzerland
5 Center for Memory and Recording Research, University of California San Diego,
La Jolla, CA 92093-0401, USA
* Correspondence: o.mounkachi@gmail.com
Received: 22 March 2019; Accepted: 16 May 2019; Published: 28 May 2019
Abstract:We investigated the magnetic and magnetocaloric properties of Gd100-xCox(x= 40 to 56)
thin films fabricated by the sputtering technique. Under an applied field change∆H=20 kOe , the magnetic entropy change(∆Sm)decreases from 2.64 Jkg−1K−1for x= 44 to about 1.27 Jkg−1K−1for
x= 56. Increasing the Co concentration from x = 40 to 56 shifts the Curie temperature of Gd100-xCox
(x= 40 to 56) thin films from 180 K toward 337 K. Moreover, we extracted the values of critical parameters Tc,β, γ, and δ by using the modified Arrott plot methods. The results indicate the presence
of a long-range ferromagnetic order. More importantly, we showed that the relative cooling power (RCP), which is a key parameter in magnetic refrigeration applications, is strongly enhanced by changing the Co concentration in the Gd100-xCoxthin films. Our findings help pave the way toward
the enhancement of the magnetocaloric effect in magnetic thin films.
Keywords: magnetocaloric effects (MCE); thin films; universal scaling analysis; critical exponents
1. Introduction
The study of the magnetocaloric effect as a means for magnetic cooling has attracted rising interest due to the prospect of replacing conventional refrigeration systems [1,2]. Recently, various experimental and theoretical works have been carried out on magnetic materials showing a large magnetocaloric effect [3,4]. Moreover, many studies of the magnetocaloric effect (MCE) for ambient applications have been performed on rare-earth based compounds, since the latter show high magnetic moments. However, the MCE was found to be rather small for this class of material. Indeed, the largest MCE was reported for the rare-earth element Gd, where the∆SMvalue goes up to −9.8 Jkg−1K−1and∆Tadnear
Tc= 293 K is about 11.6 K for a magnetic field change of 5T [5]. In 1997, Pecharsky and Gschneidner
demonstrated in their pioneering work a giant MCE in the compound Gd5Si2Ge2[6], a discovery
that reawakened interest in magnetic refrigeration for ambient applications. Later, several different classes of materials were found to exhibit giant MCEs near room temperature, such as MnAs1-xSbx[7],
Crystals 2019, 9, 278 2 of 10
La(Fe1-xSix)13[8] and their hydrides [9], MnFeP1-xAsx[10], as well as Ni0.5Mn0.5-xSnx[11]. However,
most these investigations were limited to the investigation of the MCE in bulk materials, while works on magnetic thin films are very limited.
Recently, the study of the MCE in thin films has triggered more interest, namely the study of Gd/W multilayers [12,13], manganites [14,15], FeRh [16], NiMnGa [17], and MnAs [18]. From a technological point of view, the use of magnetic refrigerant in the form of thin films, powders, or wires is more desirable [5,19–21]. In this context, many magnetic coolers based on Gd powders and laminate structures were demonstrated [1]. More recently, many studies have investigated the effect of the dimensionality reduction on MCE parameters [13,22–24]. Indeed, it was recently reported that the reduction of dimensionality in a ferromagnetic material broadens the paramagnetic to ferromagnetic (PM-FM) transition, shifts it to lower temperatures, and also reduces the magnetization saturation and magnitude of(∆Sm)[22]. On the other hand, the broadening of(∆Sm)in thin films should enhance
the relative cooling power (RCP), which is preferable for magnetic refrigeration. In this work, we have investigated the impact of the substitution of gadolinium with cobalt in thin film form on the magnetic and magnetocaloric properties of Gd100-xCoxalloys. We have developed and optimized
the magnetic properties of Gd100-xCoxthin film alloys deposited by sputtering techniques, and then
derived temperature dependence of the entropy change [25].
2. Experimental Method
The thin films were deposited at room temperature on (100)-silicon substrates by the sputtering deposition technique. The chamber base pressure was 10−7Torr. A 3 nm-thick Ta layer was used as a buffer layer, while a 3 nm-thick Ta capping layer was used to prevent the oxidation of the rare-earth elements. The deposition rates for Gd and Co targets at 50 W and 100 W were 0.719 Å/s and 0.456 Å/s, respectively. The thickness of Gd100−xCox(40< x < 56) alloy films was kept constant
and equal to 100 nm in order to ease the comparison of the magnetocaloric values. The Gd100−xCox
(40< x < 56) alloy films mostly consisted of an amorphous phase, as depicted in the measured XRD patterns (see Supplementary Materials, Figure S1 for XRD patterns of the studied Gd-Co alloy thin films). The magnetic characterization was carried out using a Quantum Design© SQUID-VSM, where the magnetic field is applied in the sample plane.
3. Results and Discussion
3.1. Magnetic Properties
We measured the temperature dependence of magnetization for all the studied alloy films to determine the temperature as well as the nature of the transition. Figure1a shows the temperature dependence of the magnetization obtained under an applied magnetic field of 500 Oe for Gd100−xCox
alloy films with different Co concentrations x = 56, 52, 48, 44, and 40. The PM-FM transition temperature Tcshown in the inset corresponds to the minimum of dM/dT. The obtained values for Tcare 190 K
for Gd60Co40, 205 K for Gd56Co44, 240 K for Gd52Co48, 282 K for Gd48Co52, and 335 K for Gd44Co56,
respectively. It can be clearly seen from Figure1b that the Tcof the studied Gd100−xCoxalloy films
increases as a function of the Co concentration x, which is mainly due to the strong Co–Co ferromagnetic exchange interaction. Indeed, any nearest neighbor of Co interacts ferromagnetically regardless of the crystal structure [26].
Crystals 2019, 9, 278Crystals 2018, 8, x FOR PEER REVIEW 3 of 10 3 of 10
Figure 1. (a) Temperature dependence of magnetization in the studied Gd100−xCox alloys for various
compositions under an applied field of 500 Oe. The inset shows the derivative curves of dM/dT as a function of T. (b) Evolution of Tc as a function of the Co concentration x.
3.2. Magnetocaloric Effect Properties
Figure 2a shows isothermal magnetization M (H) curves measured for Gd56Co44 alloy film under
an applied magnetic field up to Δ =H 20kOe and a temperature ranging from 150 to 290 K. The magnetization curves below the Tc show a non-linear behavior with a tendency towards saturation
under the applied magnetic field, which indicates a ferromagnetic behavior. However, the magnetization above the Tc shows a linear behavior, which reflects a paramagnetic behavior. The
latter is due to the thermal agitation which disarranges the magnetic moments. In order to determine the nature of the transition in Gd56Co44 alloy film, we used the Arrott plot method and employed the
Inoue-Shimizu model [28]. According to the Banerjee criteria [29], the positive (resp. negative) slope of the M2 (H/M) curves indicates a second- (resp. first-) order transition. As shown in Figure 2b, only
positive slopes of the M2 (H/M) curves were observed for the Gd56Co44 alloy film, indicating that the
PM-FM transition is a second order transition.
Figure 2. (a) Magnetization isotherms curves and (b) Arrott plots of isotherms in the vicinity of Tc for the Gd56Co44 alloy film.
Based on the magnetization curves shown in Figure 2a, the isothermal magnetic entropy change caused by the variation of the applied magnetic field from 0 to Δ =H 20kOe can be determined by using the Maxwell relation:
1 1 0 0 1 ( , ) ( , ) ( , ) i i i i M i i i M T H M T H S T H T T μ + + + − Δ = −
Figure 1.(a) Temperature dependence of magnetization in the studied Gd100−xCoxalloys for various
compositions under an applied field of 500 Oe. The inset shows the derivative curves of dM/dT as a function of T. (b) Evolution of Tcas a function of the Co concentration x.
3.2. Magnetocaloric Effect Properties
Figure2a shows isothermal magnetization M (H) curves measured for Gd56Co44 alloy film
under an applied magnetic field up to ∆H = 20 kOe and a temperature ranging from 150 to 290 K. The magnetization curves below the Tcshow a non-linear behavior with a tendency towards
saturation under the applied magnetic field, which indicates a ferromagnetic behavior. However, the magnetization above the Tcshows a linear behavior, which reflects a paramagnetic behavior. The latter
is due to the thermal agitation which disarranges the magnetic moments. In order to determine the nature of the transition in Gd56Co44alloy film, we used the Arrott plot method and employed the
Inoue-Shimizu model [27]. According to the Banerjee criteria [28], the positive (resp. negative) slope of the M2(H/M) curves indicates a second- (resp. first-) order transition. As shown in Figure2b, only positive slopes of the M2(H/M) curves were observed for the Gd56Co44alloy film, indicating that the
PM-FM transition is a second order transition.
Crystals 2018, 8, x FOR PEER REVIEW 3 of 10
Figure 1. (a) Temperature dependence of magnetization in the studied Gd100−xCox alloys for various
compositions under an applied field of 500 Oe. The inset shows the derivative curves of dM/dT as a function of T. (b) Evolution of Tc as a function of the Co concentration x.
3.2. Magnetocaloric Effect Properties
Figure 2a shows isothermal magnetization M (H) curves measured for Gd56Co44 alloy film under
an applied magnetic field up to Δ =H 20kOe and a temperature ranging from 150 to 290 K. The magnetization curves below the Tc show a non-linear behavior with a tendency towards saturation
under the applied magnetic field, which indicates a ferromagnetic behavior. However, the magnetization above the Tc shows a linear behavior, which reflects a paramagnetic behavior. The
latter is due to the thermal agitation which disarranges the magnetic moments. In order to determine the nature of the transition in Gd56Co44 alloy film, we used the Arrott plot method and employed the
Inoue-Shimizu model [28]. According to the Banerjee criteria [29], the positive (resp. negative) slope of the M2 (H/M) curves indicates a second- (resp. first-) order transition. As shown in Figure 2b, only
positive slopes of the M2 (H/M) curves were observed for the Gd56Co44 alloy film, indicating that the
PM-FM transition is a second order transition.
Figure 2. (a) Magnetization isotherms curves and (b) Arrott plots of isotherms in the vicinity of Tc for the Gd56Co44 alloy film.
Based on the magnetization curves shown in Figure 2a, the isothermal magnetic entropy change caused by the variation of the applied magnetic field from 0 to Δ =H 20kOe can be determined by using the Maxwell relation:
1 1 0 0 1 ( , ) ( , ) ( , ) i i i i M i i i M T H M T H S T H T T μ + + + − Δ = −
Figure 2.(a) Magnetization isotherms curves and (b) Arrott plots of isotherms in the vicinity of Tcfor
the Gd56Co44alloy film.
Based on the magnetization curves shown in Figure2a, the isothermal magnetic entropy change caused by the variation of the applied magnetic field from 0 to∆H=20kOe can be determined by using the Maxwell relation:
∆SM(T, H0) =µ0
X
i
Mi+1(Ti+1, H)−Mi(Ti, H)
Crystals 2019, 9, 278 4 of 10
We compared the values of –∆SMobtained for the investigated Gd100−xCoxalloys with x= 56, 52,
48, 44, and 40 with those obtained for a 100 nm-thick Gd layer, as depicted in Figure3b. The maximum values of the –∆SMpeak(T) curves are obtained close to Tc. The peak temperature in –∆SM(T) is shifted
towards high temperature by increasing x, which is most likely due to the enhancement of the Gd–Co indirect interaction. Figure3b shows the evolution of the peak entropy change value and its full width at half maximum (FWHM) as a function of the Co concentration x. It can be clearly seen that the decrease in peak –∆SMis accompanied by an increase of the FWHM. The maximal entropy change is
observed for x= 44, and is about 2.65 J/kg.K. Figure3c shows the evolution of –∆SMpeakas a function
of Tc−2/3for the investigated Gd100-xCoxalloys (x= 40, 44, 48, 52, 56) under the applied magnetic field
of 2 T. It can be seen from Figure3b that –∆SMpeakchanges linearly with Tc−2/3(or (708.8–8.83x)−2/3
with a linear correlation coefficient above 0.992), indicating that –∆SMpeakof the Gd100−xCoxalloys can
be easily tailored by adjusting x.
Crystals 2018, 8, x FOR PEER REVIEW 4 of 10
We compared the values of –ΔSM obtainedfor the investigated Gd100−xCox alloys with x = 56, 52,
48, 44, and 40 with those obtained for a 100 nm-thick Gd layer, as depicted in Figure 3b. The maximum values of the –∆SMpeak (T) curves are obtained close to Tc. The peak temperature in –∆SM (T) is shifted
towards high temperature by increasing x, which is most likely due to the enhancement of the Gd– Co indirect interaction. Figure 3b shows the evolution of the peak entropy change value and its full width at half maximum (FWHM) as a function of the Co concentration x. It can be clearly seen that the decrease in peak –∆SM is accompanied by an increase of the FWHM. The maximal entropy change
is observed for x = 44, and is about 2.65 J/kg.K. Figure 3c shows the evolution of –∆SMpeak as a function
of Tc−2/3 for the investigated Gd100-xCox alloys (x = 40, 44, 48, 52, 56) under the applied magnetic field
of 2 T. It can be seen from Figure 3b that –∆SMpeak changes linearly with Tc−2/3 (or (708.8–8.83x)−2/3 with
a linear correlation coefficient above 0.992), indicating that –∆SMpeak of the Gd100−xCox alloys can be
easily tailored by adjusting x.
Figure 3. (a) Temperature dependence of the magnetic entropy change, (b) co-concentration
dependence of the magnetic entropy change peak and the full width at half maximum (FWHM) of ΔSm (T) peak, and (c) the dependence of –∆SMpeak as a function of Tc−2/3 for the studied Gd100−xCox alloys
compounds under an applied magnetic field of 𝛥𝐻 = 20 kOe.
In addition to the isothermal entropy change, the relative cooling power (RCP) is also a key parameter to evaluate the magnetocaloric performance. The RCP considers both the isothermal magnetic entropy change and the working temperature range of magnetocaloric materials, and it is given by the following formula:
M F W H M
R C P
= − Δ
S
×
δ
T
where TFWHM is the full width at half maximum obtained from the temperature at half the maximum
peak value of the ΔSM curve. Figure 4 shows the evolution of the RCP of the Gd100-xCox thin films as
a function of the applied magnetic field. The RCP value increases with the applied magnetic field. Moreover, all the studied Gd100−xCox alloys present a large RCP value around 140 J/kg for
Figure 3.(a) Temperature dependence of the magnetic entropy change, (b) co-concentration dependence of the magnetic entropy change peak and the full width at half maximum (FWHM) of∆Sm(T) peak, and
(c) the dependence of –∆SMpeakas a function of Tc−2/3for the studied Gd100−xCoxalloys compounds
under an applied magnetic field of∆H=20 kOe.
In addition to the isothermal entropy change, the relative cooling power (RCP) is also a key parameter to evaluate the magnetocaloric performance. The RCP considers both the isothermal magnetic entropy change and the working temperature range of magnetocaloric materials, and it is given by the following formula:
RCP=−∆SM×δTFWHM
where TFWHMis the full width at half maximum obtained from the temperature at half the maximum
peak value of the∆SMcurve. Figure4shows the evolution of the RCP of the Gd100-xCoxthin films
Crystals 2019, 9, 278 5 of 10
Moreover, all the studied Gd100−xCoxalloys present a large RCP value around 140 J/kg for ∆H=20 kOe,
which is significantly higher than the RCP of the Gd thin films. Table1shows a summary of the present results, the MCE properties of the GdCo thin films, as well as some others reported in the literature. The high values of the RCP and –∆Sm(T) obtained for the Gd100−xCoxthin film alloys is
very promising for magnetic refrigeration applications with a wide temperature range.
Crystals 2018, 8, x FOR PEER REVIEW 5 of 10
20
H kOe
Δ = , which is significantly higher than the RCP of the Gd thin films. Table 1 shows a summary of the present results, the MCE properties of the GdCo thin films, as well as some others reported in the literature. The high values of the RCP and –∆Sm (T) obtained for the Gd100−xCox thin
film alloys is very promising for magnetic refrigeration applications with a wide temperature range.
Table 1. Magnetic and magnetocaloric properties of Gd100-xCox compounds with variation in Co
doping. Materials Tc (K) 𝜟𝑺𝑴 𝒑𝒆𝒂𝒌 𝑱/𝒌𝒈. 𝑲 20 H kOe Δ = 𝑹𝑪𝑷 𝑱/𝒌𝒈 20 H kOe Δ =
Δ
(T)H
References Gd60Co40 190 2.51 139 2 This work Gd56Co44 205 2.64 158 2 This work Gd52Co48 239 1.99 139 2 This work Gd48Co52 282 1.71 152 2 This work Gd44Co56 337 1.27 148 2 This work Gd100 280 1.97 106 2 This work Gd71Co29 amorphous ribbons 166 3.1 92.3 1 [30] Gd62Co38 amorphous ribbons 193 2.8 81.4 1 [30]Figure 4. Relative cooling power (RCP) as a function of the applied magnetic field for the Gd100−xCox
alloy films.
3.3. Universal Scaling Analysis
Universal scaling analysis indicates that the Co helps to homogenize the magnetic properties in GdCo thin films [25]. Such a method should remove the temperature and field dependence of the set of Δ ΔS( H T, ) curve (for fixed
Δ
H
), so that all curves processed with the same scaling protocol collapse onto a single universal curve. A failure to display this universal collapse can be attributed to material inhomogeneity [31], likely in the form of a distribution of exchange energies. Figure 5 shows the universal curve construction for each of the studied Gd100−xCox thin films by plotting ΔS’ againstθ, where ' / peak M M
S S S
Δ = Δ Δ is the rescaled entropy change and θ is the rescaled temperature variable as follows: 1 2 ( ) / ( ) ( ) / ( ) C r C C C r C C T T T T T T T T T T T T θ= − − − ≤ − − ≥
with Tr1 and Tr2 are reference temperatures chosen at 50% ofΔSmaxabove Tc. As shown in Figure 5, the
curves do not collapse into one single curve. Moreover, one can see from Figure 5 that the degree of collapse increases with the Co concentration. It has been shown that a failure to collapse (such as seen for
x
= 44) can be attributed to inhomogeneity within the material.Figure 4.Relative cooling power (RCP) as a function of the applied magnetic field for the Gd100−xCox
alloy films.
Table 1.Magnetic and magnetocaloric properties of Gd100-xCoxcompounds with variation in Co doping.
Materials Tc(K) −∆Speak M (J/kg.K) ∆H = 20kOe RCP (J/kg) ∆H = 20kOe ∆H(T) References Gd60Co40 190 2.51 139 2 This work Gd56Co44 205 2.64 158 2 This work Gd52Co48 239 1.99 139 2 This work Gd48Co52 282 1.71 152 2 This work Gd44Co56 337 1.27 148 2 This work Gd100 280 1.97 106 2 This work Gd71Co29 amorphous ribbons 166 3.1 92.3 1 [29] Gd62Co38 amorphous ribbons 193 2.8 81.4 1 [29]
3.3. Universal Scaling Analysis
Universal scaling analysis indicates that the Co helps to homogenize the magnetic properties in GdCo thin films [25]. Such a method should remove the temperature and field dependence of the set of∆S(∆H, T)curve (for fixed∆H), so that all curves processed with the same scaling protocol collapse onto a single universal curve. A failure to display this universal collapse can be attributed to material inhomogeneity [30], likely in the form of a distribution of exchange energies. Figure5shows the universal curve construction for each of the studied Gd100−xCoxthin films by plotting∆S0against
θ, where∆S0=∆SM/∆SpeakM is the rescaled entropy change and θ is the rescaled temperature variable
as follows:
θ=
( −
(T − TC)/(Tr1−TC) T ≤ TC
(T − TC)/(Tr2−TC) T ≥ TC
with Tr1and Tr2are reference temperatures chosen at 50% of∆Smaxabove Tc. As shown in Figure5,
Crystals 2019, 9, 278 6 of 10
of collapse increases with the Co concentration. It has been shown that a failure to collapse (such as seen for x= 44) can be attributed to inhomogeneity within the material.
Crystals 2018, 8, x FOR PEER REVIEW 6 of 10
Figure 5. The normalized entropy changes as a function of the rescaled temperature
θ
for different applied fields for Gd100-xCox (a)x
= 44, (b)x
= 48, (c)x
= 52, and (d)x
= 56 thin films.3.4. Critical Exponents
The second-order ferromagnetic to paramagnetic transition near the Curie temperature can be characterized by a set of critical exponents, where
β
corresponds to the spontaneous magnetization,γ
corresponds to the initial susceptibility, andδ
corresponds to the critical magnetization isotherm at Tc. The critical exponents possess the following power-law dependences [32]:0 (0, ) , 0 s M T =m
ε
βε
≤ (1) 1 0 0 0 (0, )T h , 0 m γχ
− =ε
ε
≥ (2)where
ε
= −
(
T T
c) /
T
c is the reduced temperature, andm
0 and0 0
h
m
are the critical amplitudes.Initial values of
β
=
0.4
andγ
=
1.33
are selected, then a plot ofM
1/βas a function of1/
( / )
H M
γwas obtained [12]. The high field linear region (H > 1) is used for the analysis, because the Modified Arrott Plots (MAPs) tend to deviate from linearity at low field due to the mutually misaligned magnetic domains. The values of
M
s and1 0
χ
−can be then determined from the intersection of the linearly extrapolated curves with the
M
1/β and1/
( /
H M
)
γ, respectively. Figure 6a shows the temperature dependence of
1 0
( )
T
χ
−and
M T
s( )
, which are fitted with Equations (1) and (2). The fitting enables us to obtain new values ofβ
andγ
, which are then used to construct new MAPs. These steps are therefore repeated until the iterations converge to the optimum values ofβ
,γ
, and Tc. Therefore, the MAPs shown in Figure 6a yielded the following results: β = 0.47 ± 0.009 andγ = 1.15 ± 0.1. Figure 6b depicts the modified Arrott plots, which show that all lines are parallel to
Figure 5. The normalized entropy changes as a function of the rescaled temperatureθ for different applied fields for Gd100-xCox(a) x= 44, (b) x = 48, (c) x = 52, and (d) x = 56 thin films.
3.4. Critical Exponents
The second-order ferromagnetic to paramagnetic transition near the Curie temperature can be characterized by a set of critical exponents, whereβ corresponds to the spontaneous magnetization, γ corresponds to the initial susceptibility, andδ corresponds to the critical magnetization isotherm at Tc.
The critical exponents possess the following power-law dependences [31]:
Ms(0, T) =m0|ε|β,ε ≤ 0 (1) χ−1 0 (0, T) = h0 m0 |ε|γ,ε ≥ 0 (2)
whereε= (T − Tc)/Tcis the reduced temperature, and m0andmh00 are the critical amplitudes. Initial values of β = 0.4 and γ = 1.33 are selected, then a plot of M1/β as a function of (H/M)1/γwas obtained [12]. The high field linear region (H> 1) is used for the analysis, because the Modified Arrott Plots (MAPs) tend to deviate from linearity at low field due to the mutually misaligned magnetic domains. The values of Ms andχ−10 can be then determined from the intersection of the linearly
extrapolated curves with the M1/β and(H/M)1/γ, respectively. Figure6a shows the temperature dependence ofχ−10 (T)and Ms(T), which are fitted with Equations (1) and (2). The fitting enables us to
obtain new values ofβ and γ, which are then used to construct new MAPs. These steps are therefore repeated until the iterations converge to the optimum values of β, γ, and Tc. Therefore, the MAPs
shown in Figure6a yielded the following results: β=0.47 ± 0.009 and γ=1.15 ± 0.1. Figure6b depicts the modified Arrott plots, which show that all lines are parallel to each other. On the other hand, the
Crystals 2019, 9, 278 7 of 10
fitting of the M-H measured at T close to Tcusing Equation (3) enables to extract the value of the
critical component δ:
H=DMδ, t=0 (3)
Crystals 2018, 8, x FOR PEER REVIEW 7 of 10
each other. On the other hand, the fitting of the M-H measured at T close to Tc using Equation (3)
enables to extract the value of the critical component
δ
:, 0
H =DMδ t= (3)
Figure 6. (a) Spontaneous magnetization and inverse of initial susceptibility vs. temperature, (b)
modified Arrott plot isotherms of M1/β~ (H M/ )1/γ with the calculated exponents, (c) isothermal M
(H) plots with the log–log scale at Tc= 210 K, and (d) scaling plot with
M (H,ε) ε
-β versus( )
Hε−β γ+
below and above Tc using exponent determined from the modified Arrott plot of Gd56Co44 alloy film.
Figure 6c shows the magnetic field dependence of magnetization at Tc for Gd56Co44 alloy film,
while the critical isotherm on a log–log scale is shown in the inset. The extracted value of δ is 3.37 ± 0.001. δ can also be extracted via the Widom scaling relation [33]:
1
γ
δ
= +
β
By using the critical parameters
β
andγ
obtained via the MAPs, we deduce from the Widom scaling relation a δ value of 3.44, thus confirming the reliability of the critical exponents extracted from the experimental data. Moreover, the reliability ofβ
andγ
can be confirmed via the following scaling hypothesis:( , )
( /
)
M H
ε ε
βf H
ε
β γ+ ±=
where
f
± are regular analytical functions withf
+andf
− for above and below Tc, respectively. Thescaling relation indicates that
M (H,ε) ε
-β as a function( )
H
ε
− +β γshould yield two universally
Figure 6. (a) Spontaneous magnetization and inverse of initial susceptibility vs. temperature,
(b) modified Arrott plot isotherms of M1/β~(H/M)1/γwith the calculated exponents, (c) isothermal M (H) plots with the log–log scale at Tc= 210 K, and (d) scaling plot with M(H, ε)ε−βversus Hε−(β+γ)
below and above Tcusing exponent determined from the modified Arrott plot of Gd56Co44alloy film.
Figure6c shows the magnetic field dependence of magnetization at Tcfor Gd56Co44alloy film,
while the critical isotherm on a log–log scale is shown in the inset. The extracted value of δ is 3.37 ± 0.001. δ can also be extracted via the Widom scaling relation [32]:
δ=1+γ
β
By using the critical parametersβ and γ obtained via the MAPs, we deduce from the Widom scaling relation aδ value of 3.44, thus confirming the reliability of the critical exponents extracted from the experimental data. Moreover, the reliability ofβ and γ can be confirmed via the following scaling hypothesis:
M(H,ε) =εβf±(H/εβ+γ)
where f±are regular analytical functions with f+and f−for above and below Tc, respectively. The
scaling relation indicates that M(H, ε)ε−βas a function Hε−(β+γ)should yield two universally different branches, one for T> Tcand the other for T< Tc. By using the values ofβ, γ, and Tcfrom the MAPs
Crystals 2019, 9, 278 8 of 10
for T> Tcand the other for T< Tc, which agrees with the scaling theory and confirms that the obtained
values for the critical exponents and Tcare reliable. Moreover, these critical exponents are very similar
to the theoretical values from the mean field model (γ = 1.0, β = 0.5, and δ = 3) [33]. We also analyzed the critical behavior of magnetic phase transition using Arrott plots for Gd100−xCox(x= 40, 48, 52, and
56), which follows the mean field model. Consistent with the existence of long-range ferromagnetic interaction, the critical behavior analysis in the vicinity of Tcdemonstrates that the magnetism of the
GdCo thin films is governed by the long range nature of ferrimagnetism in this system.
4. Conclusions
In summary, we fabricated Gd100−xCoxalloy films on a silicon substrate using sputtering techniques.
The magnetic and magnetocaloric effect of Gd100-xCox(x= 44, 48, 52, 56) thin films were investigated.
The Curie temperature increases with the Co concentration, and the maximal magnetic entropy change reaches a maximum at the Curie temperature. Under an applied magnetic field of∆H=20 kOe, the value of –∆SMis found to be 2.64 for x= 44. Moreover, the studied Gd100−xCoxalloy films present an
important relative cooling power (RCP) higher than 140 J/kg. Moreover, the investigation of the critical properties of the second-order ferromagnetic transition of the Gd100−xCoxalloy films demonstrate
that the magnetic interaction around Tccan be described with the mean field model corresponding to
long-range interaction.
Supplementary Materials:The following are available online athttp://www.mdpi.com/2073-4352/9/6/278/s1.
Author Contributions: Conceptualization, S.M., C.-H.L., M.S.E.H., O.M. and A.B.; methodology, C.-H.L. and
M.T.; formal analysis, M.T. and C.-H.L.; investigation, M.T. and C.-H.L.; writing—original draft preparation, M.T. and O.M.; writing—review and editing, M.S.E.H., M.T. and O.M.; visualization, M.S.E.H. and M.T.; supervision, S.M., O.M., A.B., M.H., and M.B.
Funding:This work was funded by the MESRSFC in the framework of the national program PPR under contract
No. PPR/2015/57 and by PHC Toubkal/17/49 project.
Acknowledgments:We would like to thank S. Suire, C.-S. Chang, and T. Hauet for technical assistance with the SQUID-VSM measurements.
Conflicts of Interest:The authors declare no conflict of interest.
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